An Introduction to OpenEpi

Version 3.0.1

by

Kevin M. Sullivan, PhD, MPH, MHA

Andrew G. Dean, MD, MPH

Minn Minn Soe, MD, MCTM, MPH

August 18 2014

TABLE OF CONTENTS

Introduction . . . . . . . . . . . . . . . 1

Considerations and Issues in Using OpenEpi . . . . . . 3

Running OpenEpi on the Web vs. Downloading . . . . . 4

Options and Settings . . . . . . . . . . . . 5

Copying and Pasting results . . . . . . . . . . 10

Using OpenEpi on PDA’s and cell phones . . . . . . 11

An Introduction to the structure of OpenEpi modules . . . . 12

Calculator . . . . . . . . . . . . . . . . 15

References . . . . . . . . . . . . . . . . 16

Appendix 1 - Comparison of OpenEpi, Epi Info, SAS, and SPSS on . 17

some statistical output

Introduction

OpenEpi (www.OpenEpi) is a free, web-based, open source, operating system-independent series of programs for use in epidemiology, biostatistics, public health, and medicine, providing a number of epidemiologic and statistical tools for summary data.(1-13) OpenEpi was developed in JavaScript and hypertext markup language (HTML) and can be run in browsers supporting these languages, such as Microsoft Explorer, Mozilla Firefox, Safari, Chrome, and Opera, on a number of operating systems, such as Microsoft Windows, Macintosh, Linux, and on an iPhone. The program can be run from the OpenEpi website or downloaded and run without a web connection. The source code and documentation is downloadable and freely available. Reviews of OpenEpi can be found in the following references.(14-17) OpenEpi has had over 8 million hits since its inception in 2003, with over 1.8 million hits in 2011 alone, from 188 countries.

The OpenEpi developers have had extensive experience in the development and testing of Epi Info, a program developed by the Centers for Disease Control and Prevention (CDC) and widely used around the world for data entry and analysis. OpenEpi was developed to perform analyses found in the DOS version of Epi Info modules StatCalc and EpiTable, to improve upon the types of analyses provided by these modules, and to provide a number of tools and calculations not currently available in Epi Info. It is the first step toward an entirely web-based set of epidemiologic software tools. OpenEpi can be thought of as an important companion to Epi Info and to other programs such as SAS, PSPP, SPSS, Stata, SYSTAT, Minitab, Epidata, and R. For a comparison of the types of cross-tabulations performed by OpenEpi, Epi Info, SAS, and SPSS, see Appendix 1. Epi Info version 3.5.3 and later versions includes a link to OpenEpi. Another functionally similar Windows-based program is Winpepi (information available at Wikipedia). Both OpenEpi and Epi Info were developed with the goal of providing tools for low and moderate resource areas of the world. The initial development of OpenEpi was supported by a grant from the Bill and Melinda Gates Foundation to Emory University.(18-19)

The types of calculations currently performed by OpenEpi include:

• Various confidence intervals for proportions, rates, standardized mortality ratio, mean, median, percentiles
• 2x2 crude and stratified tables for count and rate data
• Matched case-control analysis
• Test for trend with count data
• Independent t-test and one-way ANOVA
• Diagnostic and screening test analyses with receiver operating characteristic (ROC) curves
• Sample size for proportions, cross-sectional surveys, unmatched case-control, cohort, randomized controlled trials, and comparison of two means
• Power calculations for proportions (unmatched case-control, cross-sectional, cohort, randomized controlled trials) and for the comparison of two means
• Random number generator

For epidemiologists and other health researchers, OpenEpi performs a number of calculations based on tables not found in most epidemiologic and statistical packages. For example, for a single 2x2 table, in addition to the results presented in other programs, OpenEpi provides estimates for:

• Etiologic or prevented fraction in the population and in exposed with confidence intervals, based on risk, odds, or rate data
• The cross-product and MLE odds ratio estimate
• Mid-p exact p-values and confidence limits for the odds ratio
• Calculations of rate ratios and rate differences with confidence intervals and statistical tests.

Figure 1. OpenEpi Menu with a short description

Menu item Home Info and Help Language/Options/Settings Calculator Counts Std.Mort.Ratio Proportion Two by Two Table Dose-Response R by C Table Matched Case Control Screening Person Time 1 Rate Compare 2 Rates Continuous Variables Mean CI Median/%ile CI t test ANOVA Sample Size Proportion Unmatched CC Cohort/RCT Mean Difference Power Unmatched CC Cohort Clinical Trial X-Sectional Mean Difference Random numbers Download OpenEpi

Description The main OpenEpi page Optional settings such as language, table orientation, etc. A calculator, similar to a hand-held scientific calculator The following modules are for analysis of count data SMR - Standardized mortality (or morbidity) ratio, no. observed / no. expected Various confidence intervals for a proportion 2 x 2 tables and stratified 2 x 2 tables with p-values and estimates R x 2 tables and stratified R x 2 tables for more than 2 exposure levels General R x C table (usually for more than 2 rows/2 columns), chi-square p-value Pair-matched case-control analysis; p-values and the odds ratio Screening/diagnostic results such as sensitivity, specificity, ROC The following modules are for the analysis of person-time data Various confidence intervals for a single rate 2 x 2 tables and stratified tables with person-time data, p-values and estimates The following modules are for the analysis of continuous or ordinal data Provides a confidence interval for a mean Provides observations for a percentile and its confidence limits Calculates independent t test assuming equal & unequal variance Calculates ANOVA table and confidence limits around each group mean Sample size calculations for various study designs Absolute precision approach to sample size for a proportion Sample size calculation for an unmatched case-control study Sample size calculation for a cross-sectional, cohort, or clinical trial study Sample size for the difference between two means Power calculations for various study designs Power calculations for an unmatched case-control study Power calculations for a cohort study Power calculations for a randomized clinical trial Power calculations for a cross-sectional study Power calculations for the difference between two means Random number generator

For stratified 2x2 tables with count data, OpenEpi provides:

• Mantel-Haenszel (MH) and precision-based estimates of the risk ratio and odds ratio
• Precision-based adjusted risk difference
• Tests for interaction for the risk ratio, odds ratio, and risk difference
• Four different confidence limit methods for the odds ratio.

Similar to Epi Info, in a stratified analysis, both crude and adjusted estimates are provided so that the assessment of confounding can be made. With rate data, OpenEpi provides adjusted rate ratio’s and rate differences, and tests for interaction. Finally, with count data, OpenEpi also performs a test for trend, for both crude data and stratified data.

In addition to being used to analyze data by health researchers, OpenEpi has been used as a training tool for teaching epidemiology to students at: Emory University, University of Michigan, Morehouse College, Columbia University, University of Wisconsin, San Jose State University, University of Medicine and Dentistry of New Jersey, and elsewhere. This includes campus-based and distance learning courses. Because OpenEpi is easy to use, requires no programming experience, and can be run on the internet, students can use the program and focus on the interpretation of results.

Version 2.2 of OpenEpi was released Nov 11 2007 with the improvement of being able to run in English, French, Spanish, or Italian. In progress are translations into Portuguese and Chinese.

Comments and suggestions for improvements are welcomed and the developers respond to user queries. The developers encourage others to develop modules that could be added to OpenEpi and provide a developer’s tool at the website. Planned future developments include improvements to existing modules, development of new modules, and add the ability to cut and paste data and/or read data files.

We encourage those in public health to use OpenEpi and to share their experiences with the developers. Comments and suggestions for improvements are welcome and we respond to user queries. We encourage others to develop modules that could be added to OpenEpi and we provide a developer’s tool at the website. The developers are currently seeking funding to improve the existing modules, develop new modules, translate into other languages, and add the ability to cut and paste data and/or read data files.

Should you use OpenEpi results in a report or publication, we suggest you use the following reference:

Dean AG, Sullivan KM, Soe MM. OpenEpi Version 3.0.1: Open Source Epidemiologic Statistics for Public Health. Updated Apr 6, 2013, www.OpenEpi.com, accessed (date).

Please be sure to use the correct “updated” date which is on the main OpenEpi screen near the center bottome of the screen; the date of Apr 6, 2013 was the most recent version at the time of this writing. Also list the date in which OpenEpi was accessed for your analyses.

Finally, we would like to note that OpenEpi may not always operate as expected because of different operating systems, different browsers, and different levels of computer security. Most of our testing of OpenEpi is under the Windows environment using Microsoft Explorer and Mozilla Firefox. If you run into unexpected problems, please let us know and provide: the operating system and version number; browser name and version number; type of computer/PDA/phone used; antivirus and popup blocker software installed on computer; whether you have administrative rights on the computer; and exact details of the problem with a screen shot and the steps taken prior to the error.

Considerations and Issues in Using OpenEpi

Below are some issues in using OpenEpi which are reviewed next:

· Running OpenEpi on the Web vs. Downloading

· Options and Settings

· Copying and Pasting results

· Using OpenEpi on PDA’s and cell phones

Running OpenEpi on the Web vs. Downloading

The easiest way to use OpenEpi is to open a browser on a computer linked to the internet and go to www.OpenEpi.com. You may consider downloading OpenEpi to your computer for the following reasons:

· Your access to the internet is limited, intermittent, or slow

· To have OpenEpi available when offline, such as for portable computers while traveling

· You want to review the source code and modify it for your own use

· Occasionally the server on which OpenEpi resides may not work for short periods of time

For those who travel, you might want to install OpenEpi on your portable computer or PDA so that you can use it without requiring an internet connection. For those living in areas with infrequent or slow internet access, you might consider installing OpenEpi on your computer. You can copy OpenEpi to a USB memory stick or a CD ROM.

Another reason to download OpenEpi is that some users might be JavaScript programmers and interested in reviewing the source code and perhaps modifying the code. We encourage JavaScript programmers to send suggestions and/or updated code to the OpenEpi developers for recommended improvements or for new types of calculations.

To download OpenEpi, click on Download OpenEpi in the left command window and the information is present as shown in Figure 2. Download a “.zip” file to your computer and use a program to “unzip” the files to your computer, an option that works under most operating systems.

Figure 2. Download OpenEpi screen

Using the mouse, left click on OpenEpi.ZIP (see Figure 2). For most users a dialog box may appear asking if you want to save or open the .zip file. You can either save the .zip file to your computer and then open the .zip file using a .zip utility program or, if you have a zip utility program on your computer, open the .zip file. Additional information on zip files can be found at en.wikipedia.org/wiki/ZIP_(file_format). When the .zip file is “unzipped” or “uncompressed”, you will need to specify where to place the files. Frequently the files are saved on the “C:” drive in a folder called “OpenEpi”, however you can save the files into whichever drive and folder you prefer. To start OpenEpi, open the folder where the OpenEpi files were uncompressed, and click on the file “Index.htm”.

Options and Settings

There are a number of options and settings that can be selected in OpenEpi. To see these, click on the “Options/Setting” option in the menu on the left side of the screen and the OpenEpi Settings screen will be presented (Figure 3). The options/settings are:

· Language

· Settings for 2 x 2 Input Table (“table orientation”)

· Confidence level for confidence intervals

· Provide the following in the output:

o Do Not Highlight “significant” p-values

o Show column percents

o Show row percents

o Show input datatables

o Show stratum results

Language: As of this writing, the languages supported by OpenEpi are English, French, Italian, and Spanish. As languages are added, they will be added to the Select Language pull down menu as shown in Figure 3. If you switch languages, you will most likely need to use the “refresh” button on the browser to change the language on the current screen.

Figure 3. OpenEpi Settings screen

Layout - Settings for a 2 x 2 Input Table: This option allows the user to specify whether disease forms the columns and exposure the rows, or vice versa. It also allows the user to specify the order of those with the event, i.e. “(+)”, or without the event, i.e. “(-). Different textbooks and different software programs may have different ways in which a 2 x 2 table is presented. The “Epi Info; Schlesselman; Lilienfeld; Friis” automatic layout is as follows:

	Disease
Exposed	(+)	(-)	Total
(+)	a	b	a+b
(-)	c	d	c+d
Total	a+c	b+d	a+b+c+d

From this table orientation, the odds ratio (OR), risk ratio (RR), and risk difference (RD) in the above table can be calculated as:

OR = (a*d) / (b*c) RR = [a/(a+b)] / [c/(c+d)] RD = [a/(a+b)] - [c/(c+d)]

The previous table layout is also the expected format in SAS and SPSS for “Column 1 Risk” calculations. It is up to the user to make sure the table orientation is correct for the data so that the odds ratio, risk ratio, and other epidemiologic parameter estimates are calculated correctly. The “Kleinbaum; Breslow/Day” automatic layout is as follows, with disease forming the rows and exposure the columns:

	Exposed
Disease	(+)	(-)	Total
(+)	a	b	a+b
(-)	c	d	c+d
Total	a+c	b+d	a+b+c+d

There are eight possible ways to orient a 2 x 2 table (see Table 1). For a given definition of disease and exposure, only one of these tables will provide the correct risk ratio and risk different estimates. For the odds ratio there are two possibilities: the correct odds ratio and the inverse of the odds ratio (1/OR).

Here is the suggested way to use this option. First, click on Language/Options/Settings in the left menu screen, adjust the table orientation to your preference, then go to the Two by Two Table menu option and the input table orientation should be as just set in the options/settings. Note that OpenEpi writes a cookie to the computer (if allowed) to remember the options/settings so they will not change unless the user changes these settings. Also note that when the table orientation is changed when data are in an input table, data in the input table will be erased. Another place where the options/settings can be changed is from the input window of some of the OpenEpi modules. An example is presented in Figure 4 for the Two by Two Table, just below the Clear button where it says “Settings”. Also note that the output in the Results window will be in the same layout as the input table as specified in the Options/Settings.

Figure 4. Example of how to go to the Settings/Options screen from Two by Two Table data input module

Table 1. Eight possible ways to arrange a 2x2 table on Disease and Exposure status

Disease Status in Columns, Exposure Status in Rows

1. Correct – Epi Info, SAS (col 1 risk), SPSS (col 1 risk)				2. Disease Columns Switched
	Disease				Disease
Exposed	(+)	(-)	Total	Exposed	(-)	(+)	Total
(+)	27	13	40	(+)	13	27	40
(-)	19	16	35	(-)	16	19	35
Total	46	29	75	Total	29	46	75
	OR = 1.75	RR = 1.24			“OR” =0.57	“RR” =0.71

3. Exposure Rows Switched				4. Both Disease & Exposure Switched
	Disease				Disease
Exposed	(+)	(-)	Total	Exposed	(-)	(+)	Total
(-)	19	16	35	(-)	16	19	35
(+)	27	13	40	(+)	13	27	40
Total	46	29	75	Total	29	46	75
	“OR” =0.57	“RR” =0.80			“OR” =1.75	“RR” =1.41

Disease Status in Rows, Exposure Status in Columns (which is incorrect in Epi Info, SAS, and SPSS)

5. (+) in First Column/Row				6. Exposure Columns Switched
	Exposed				Exposed
Disease	(+)	(-)	Total	Disease	(-)	(+)	Total
(+)	27	19	46	(+)	19	27	46
(-)	13	16	29	(-)	16	13	29
Total	40	35	75	Total	35	40	75
	“OR” =1.75	“RR” =1.31			“OR” =0.57	“RR” =0.75

7. Disease Rows Switched				8. Both Disease & Exposure Switched
	Exposed				Exposed
Disease	(+)	(-)	Total	Disease	(-)	(+)	Total
(-)	13	16	29	(-)	16	13	29
(+)	27	19	46	(+)	19	27	46
Total	40	35	75	Total	35	40	75
	“OR” =0.57	“RR” =0.80			“OR” =1.75	“RR” =1.34

(+)=”Yes” or present; (-)=”No” or absent

Confidence level for confidence intervals: Ninety five percent confidence intervals are the default, but users can select from a list of other confidence levels (See Figure 5). In some of the data input modules the confidence level is presented (see Figure 4 below the Clear button and Settings as an example). The output in the Results screen will also specify the confidence level.

Figure 5. Confidence level options in the Options/Settings screen

Do Not highlight “significant” p-values: If this box is checked, all p-values and confidence intervals are presented in a black font. If this box is not checked, p-values <0.05 and confidence intervals that do not capture the null value are presented in a blue font – all others will be in a black font. There will also be the following message in the output:

P-values < 0.05 and confidence limits excluding null values (0,1, or [n]) are highlighted.

Show column percents, row percents, input tables, stratum results: This option applies to the Two x Two Tables and Compare Two Rates modules. At this time it appears that the Show input datatables and Show stratum results are always on, that is, the data tables and stratum results are also presented in the results. For Show column percents and Show row percents, the cell counts and percentages are shown. The cell counts are represented in bold numbers in the larger font in the table below.

Unstratified (Crude) Values
		'Disease'
		(+)	(-)
	(+)	205	89	294
		69.7%	30.3%	100%
		61.4%	50.9%
'Exposure'	(-)	129	86	215
		60%	40%	100%
		38.6%	49.1%
		334	175	509
		65.6%	34.4%	100%
		100%	100%

The marginal counts - row, column, and total, are represented in bold numbers in the larger font in the table below:

Unstratified (Crude) Values
		'Disease'
		(+)	(-)
	(+)	205	89	294
		69.7%	30.3%	100%
		61.4%	50.9%
'Exposure'	(-)	129	86	215
		60%	40%	100%
		38.6%	49.1%
		334	175	509
		65.6%	34.4%	100%
		100%	100%

The row percents are represented in bold numbers in the larger font in the table below:

Unstratified (Crude) Values
		'Disease'
		(+)	(-)
	(+)	205	89	294
		69.7%	30.3%	100%
		61.4%	50.9%
'Exposure'	(-)	129	86	215
		60%	40%	100%
		38.6%	49.1%
		334	175	509
		65.6%	34.4%	100%
		100%	100%

The column percents are represented in bold numbers in the larger font in the table below:

Unstratified (Crude) Values
		'Disease'
		(+)	(-)
	(+)	205	89	294
		69.7%	30.3%	100%
		61.4%	50.9%
'Exposure'	(-)	129	86	215
		60%	40%	100%
		38.6%	49.1%
		334	175	509
		65.6%	34.4%	100%
		100%	100%

If stratified data are entered, the results by stratum are presented as well as a “crude” table which combines the stratified tables into one table as shown on the next page:

2 x 2 Table Statistics

Values for Stratum 1
		'Disease'
		(+)	(-)
	(+)	66	28	94
		70.2%	29.8%	100%
		64.7%	46.7%
'Exposure'	(-)	36	32	68
		52.9%	47.1%	100%
		35.3%	53.3%
		102	60	162
		63%	37%	100%
		100%	100%

Values for Stratum 2
		'Disease'
		(+)	(-)
	(+)	139	61	200
		69.5%	30.5%	100%
		59.9%	53%
'Exposure'	(-)	93	54	147
		63.3%	36.7%	100%
		40.1%	47%
		232	115	347
		66.9%	33.1%	100%
		100%	100%

Unstratified (Crude) Values
		'Disease'
		(+)	(-)
	(+)	205	89	294
		69.7%	30.3%	100%
		61.4%	50.9%
'Exposure'	(-)	129	86	215
		60%	40%	100%
		38.6%	49.1%
		334	175	509
		65.6%	34.4%	100%
		100%	100%

Copying and Pasting results

OpenEpi presents the results in their own window in HTML. You may want to copy information in the results window to a word processor, such as Word, or print the results. Printing is relatively easy, just use the print function of the browser. To copy and paste data, in Windows, you “block” or “select” the data, that is, move the mouse to the top of the results that you want to copy, hold the left button and move the mouse to the bottom of the output you wish to copy. Next to copy the data, you can press the control key (“Ctrl”) and the “c” key (“c”) simultaneously, e.g., Ctrl+C. This will copy the data to the clipboard. (Note: an alternative method is after you have selected the data, from the Internet Explorer (or other browser) menu, click on Edit and then Copy, or right click in the highlighted area and a small menu should appear and click on Copy.) Next, open the word processor, place the cursor where you want to paste the data, and press Ctrl+V (or, alternatively, from the word processing menu Edit and then Paste). Once in the word processor you can change font sizes and make other modifications to the results.

For those who have installed OpenEpi onto their computer using OpenEpi.MSI (and are therefore using Windows), one of the icons labeled “OpenEpi SAVE”. By clicking on this icon to run OpenEpi all of the output will automatically be saved into the folder …OpenEpi\RESULTS.

Using OpenEpi on PDA’s and cell phones

OpenEpi works on some PDA’s and cell phones, although OpenEpi was not developed with small screens in mind. We have been able to use OpenEpi on an iPhone, iPad, iPod, Nook, and other smaller devices. Whether OpenEpi will work on a PDA or cell phone depends on the extent to which the browser can run JavaScript. Open the browser and go the www.OpenEpi.com and determine whether you can see both the menu and the main screen. Some browsers seem to have problems showing both the menu and main screen. If you have problems at this point, it is possible to avoid the OpenEpi menu system and to go directly to each module. The link for each module is presented in Figure 6. Also there some similar modules and other programs available at www.sph.emory.edu/~cdckms.

Figure 6. Direct website link to OpenEpi modules

Menu item Direct website link to module

Home

Info and Help

Calculator www.openepi.com/Calculator/calculator.htm

Counts

Std.Mort.Ratio www.openepi.com/SMR/SMR.htm

Proportion www.openepi.com/Proportion/Proportion.htm

Two by Two Table www.openepi.com/TwobyTwo/TwobyTwo.htm

Dose-Response www.openepi.com/DoseResponse/DoseResponse.htm

R by C Table www.openepi.com/RbyC/RbyC.htm

Matched Case Control www.openepi.com/MatchCC/MatchCC.htm

Screening www.openepi.com/DiagnosticTest/DiagnosticTest.htm

Person Time

1 Rate www.openepi.com/PersonTime1/PersonTime1.htm

Compare 2 Rates www.openepi.com/PersonTime2/PersonTime2.htm

Continuous Variables

Mean CI www.openepi.com/Mean/CIMean.htm

Median/%ile CI www.openepi.com/Median/CIMedian.htm

t test www.openepi.com/Mean/t_testMean.htm

ANOVA www.openepi.com/Mean/ANOVA.htm

Sample Size

Proportion www.openepi.com/SampleSize/SSPropor.htm

Unmatched CC www.openepi.com/SampleSize/SSCC.htm

Cohort/RCT www.openepi.com/SampleSize/SSCohort.htm

Mean Difference www.openepi.com/SampleSize/SSMean.htm

Power

Unmatched CC www.openepi.com/Power/PowerCC.htm

Cohort www.openepi.com/Power/PowerCohort.htm

Clinical Trial www.openepi.com/Power/PowerRCT.htm

X-Sectional www.openepi.com/Power/PowerCross.htm

Mean Difference www.openepi.com/Power/PowerMean.htm

Random numbers www.openepi.com/Random/Random.htm

Options/Settings www.openepi.com/Etable/Settings.htm

An Introduction to the structure of OpenEpi modules

Each of OpenEpi’s modules has a “tabbed” interface, i.e., there are a series of tabs with the names of the tabs as follows (see Figure 7):

o Start

o Enter

o Results

o Examples

o Help

A brief overview of the tabbed screens is provided in Figures 7-10.

Calculator

A calculator with higher math functions. For epidemiologists, it is somewhat better than the simple calculator that comes with Microsoft Windows. Some details on the use of the calculator are provided below.

Algebraic functions

e Mathematical constant 2.718281828459045

Pi Mathematical constant 3.141592653589793

+/- Change the sign of the number in the display from + to – or vice versa

exp e to the power of the number in the display

Example, “1” in the display, press “exp” (i.e., e¹) and the result is 2.718281828459045

Example, “2” in the display, press “exp” (i.e., e²) and the result is 7.38905609893065

log Logarithm of base 10 (log₁₀)

Example, “10” in the display, press “log” (i.e., log₁₀10) and the result is 1

Example, “100” in the display, press “log” (i.e., log₁₀100) and the result is 2

ln Natural logarithm, logarithm of base e (log_{2.718281828459045})

Example, “1” in the display, press “ln” (i.e., ln1) and the result is 2.718281828459045

Example, “2.718281828459045” in the display, press “ln” (i.e., ln2.71…) and the result is 1

sqrt Square root () of the number in the display

Example, “4” in the display, press “sqrt” and the result is 2

Example, “9” in the display, press “sqrt” and the result is 3

^ Take the number in the display to the power of another number

Example, “10” is in the display, press “^” and enter “2” (i.e., 10²) and the result is 100

Example, “4” is in the display, press “^” and enter “0.5” (i.e., 4^½) and the result is 2

1/x Inverse of the number in the display

Example, “10” is in the display, press “1/x” (i.e., 1/10) and the result is 0.1

Example, “0.5” is in the display, press “1/x” (i.e., 1/0.5) and the result is 2

Trigonometric functions

· Function

§ sin sine

§ cos cosine

§ tan tangent

· Inverse function

§ asin arcsine

§ acos arccosine

§ atan arctangent

· Hyperbolic trigonometric functions

§ cosh

§ tanh

References

1. Dean AG, Sullivan KM, Soe MM. Epi Info™ and OpenEpi in Epidemiology and Clinical Medicine: Health Applications of Free Software. Create Space Publishing, 2010.
2. Sullivan KM, Dean AG, Soe MM. OpenEpi - a web-based epidemiologic and statistical calculator for public health.. Public Health Reports (124): 471-474. 2009.

3. Sullivan K. R, WinPepi, and OpenEpi. The Epidemiology Monitor, 30(3), 2009 (March).

4. Sullivan K, Abramson J. Update on free epidemiologic software. The Epidemiology Monitor, 29(7):3-4, 2008 (July)
5. Sullivan K. Faculty Spotlight. The Epi Vanguard, Spring-Summer 2008
6. Sullivan KM. OpenEpi now available in English, French, Italian, and Spanish. The Epidemiology Monitor, 28: 14, 2007 (December)
7. Sullivan KM, Dean A, Soe MM. OpenEpi Version 2. The Epidemiology Monitor, 28 (5):1, 9-10, 2007 (May)
8. Sullivan KM. Overview Of Free Analytic Software for Epidemiologists. The Epidemiology Monitor, 28 (4): 2007 (April)
9. Sullivan KM. OpenEpi - A web-based calculator. The Epi Vanguard, Spring, 2007
10. Sullivan K, Dean A, Soe MM. OpenEpi: an update. The Epidemiology Monitor, 27 (6):4, 2006 (June)
11. Sullivan KM, Dean AG, Mir R. OpenEpi: A new collaborative effort in epidemiologic computing. The Epidemiology Monitor 25(4):3, 7, 9, 2004 (April)
12. Sullivan KM, Dean AG, Mir R. OpenEpi: a new collaborative effort in epidemiologic computing. 36th Annual Meeting of the Society for Epidemiologic Research, Atlanta GA, June 11-14, 2003.
13. Dean AG, Sullivan KM, Mir R. The Open Epi Initiative: Open Source Web Browser Software for Public Health. Annual Scientific Meeting of the International Epidemiological Association, European Epidemiology Federation, Toledo, Spain, 1-4 October 2003.
14. OpenEpi online « Technology, Health & Development
15. Great free tools for teaching statistics | Education IT | ZDNet.com
16. Antoch J. Environment for statistical computing. Computer Science Review 2(2):113-122, 2008
17. Abramson JH, Abramson ZH. Research Methods in Community Medicine: Surveys, Epidemiologic Research, Programme Evaluation, Clinical Trials, 6th Ed. John Wiley & Sons, 2008
18. Rollins School of Public Health :: Promoting Health, Preventing Disease :: Locally, Nationally, Globally: http://www.sph.emory.edu/index.php
19. Bill & Melinda Gates Foundation: http://www.gatesfoundation.org/default.htm

Appendix 1. Comparison of OpenEpi, Epi Info, SAS, and SPSS on some statistical output

Confidence intervals for a proportion and rate

Table A1.1 Comparison of Epi Info, OpenEpi, SAS, and SPSS for a single proportion or rate

	Epi Info 3.5.4	Epi Info 7.1.4	OpenEpi 3.01	SAS 9.3	SPSS 17.0
Confidence Interval Methods
Proportion
Mid-p exact	-	-	Y	-	-
Fisher’s exact (Clopper-Pearson)	Y	Y	Y	Y	-
Wald (Norm Approx)	-	-	Y	Y	Y
Modified Wald (Agresti-Coull)	-	-	Y	Y	-
Score (Wilson)	Y		Y	Y	-
Score with cc (quadratic)	-	-	Y	-	-
Rate
Mid-p exact	-	-	Y	-	-
Fisher’s exact	-	-	Y	-	-
Normal Approx	-	-	Y	Y	Y
Byar poisson	-	-	Y	-	-
Rothman/Greenland	-	-	Y	-	-

Notes: Norm Approx = normal approximation; cc = continuity correction; Epi Info will provide the Fisher exact confidence limits with “small” numbers and Score method for large numbers; In SPSS, for a proportion, with a variable coded as 1/0, use the Explore command and request options under statistics for a confidence interval. SAS and SPSS can calculate a confidence interval for a rate using the ratio command approach.

Single 2x2 Table Statistics and Parameter Estimates

Comparison of Epi Info, OpenEpi, SAS, and SPSS for single 2x2 table, count data

	Epi Info 3.5.4	Epi Info 7.1.4	OpenEpi 3.01	SAS 9.3	SPSS 17.0
Statistical Tests
χ^2Pearson, uncorrected	2 sided	2 sided	1 & 2 sided	2 sided	2 sided
χ^2Yates, corrected	2 sided	2 sided	1 & 2 sided	2 sided	2 sided
χ^2Mantel-Haenszel	2 sided	2 sided	1 & 2 sided	2 sided	2 sided
χ^2Likelihood Ratio	-		-	2 sided	2 sided
Fisher exact	1 sided	1 & 2 sided	1 & 2 sided	1 & 2 sided	1 & 2 sided
Mid-p exact	1 sided	1 sided	1 & 2 sided	-	-
Risk-based point est/CIs
Risk ratio
Approximate	Y	Y	Y	Y	Y
Exact	-	-	-	Y	-
Risk difference
Approximate	Y	Y	Y	Y	-
Exact	-	-	-	Y	-
EFp	-	-	Y	-	-
EFe	-	-	Y	-	-
PFp	-	-	Y	-	-
PFe	-	-	Y	-	-
Odds-based point est/CIs
OR cross-product	Y	Y	Y	Y	Y
OR MLE	Y	Y	Y	-	-
CI for OR
Taylor	Y	Y	Y	Y	Y
Fisher	Y	Y	Y	Y	Y
Mid-P	Y	Y	Y	-	-
EFp	-	-	Y	-	-
EFe	-	-	Y	-	-
PFp	-	-	Y	-	-
PFe	-	-	Y	-	-

Uncorr=uncorrected; MH=Mantel-Haenszel; LR=likelihood ratio; CI=confidence interval; MLE=maximum likelihood estimate; EFp=Etiologic Fraction in the population; EFe=Etiologic Fraction in the exposed; PFp=preventive fraction in the population; PFe=Prevented Fraction in the exposed

Comparison of Epi Info, OpenEpi, SAS, and SPSS for a single 2x2 table, person-time data

	Epi Info 3.5.4	Epi Info 7.1.4	OpenEpi 3.01	SAS 9.3	SPSS 17.0
Statistical Tests
Z approach (same as χ^2)	-	-	1 & 2 sided	-	-
Fisher exact	-	-	1 & 2 sided	-	-
Mid-p exact	-	-	1 & 2 sided	-	-
Point est/CIs
Rate ratio	-	-	Y	-	-
Rate difference	-	-	Y	-	-
EFp	-	-	Y	-	-
EFe	-	-	Y	-	-
PFp	-	-	Y	-	-
PFe	-	-	Y	-	-

EFp=Etiologic Fraction in the population; EFe=Etiologic Fraction in the exposed; PFp=preventive fraction in the population; PFe=Prevented Fraction in the exposed

Stratified 2x2 Table Statistics and Parameter Estimates

Comparison of Epi Info, OpenEpi, SAS, and SPSS for stratified 2x2 tables, count data

	Epi Info 3.5.4	Epi Info 7.1.4	OpenEpi 3.01	SAS 9.3	SPSS 17.0
Statistical Tests
Statistics for crude table	-	-	Y	-	-
Statistics for adjusted results
χ^2MH uncorrected	2 sided	2 sided	1 & 2 sided	2 sided	2 sided
χ^2MH corrected	2 sided	2 sided	-	-	-
Fisher exact	1 sided	-	1 & 2 sided	1 & 2 sided	-
Mid-p exact	1 sided	-	1 & 2 sided	-	-
Test for interaction
OR
Breslow-Day	-	-	-	Y	-
Woolf	Y	Y	Y	-	Y
Exact (Zelen)	-	-	-	Y	-
RR (Woolf)	Y	Y	Y	-	-
RD (Woolf)	-	-	Y	-	-
Risk-based point est/CIs
Risk ratios
Crude Risk ratio	Y	Y	Y	-	-
Adj. Risk ratio MH	Y	Y	Y	Y	-
Adj. Risk ratio precision (Logit)	-		Y	Y	-
Risk differences
Crude Risk difference	-	-	Y	-	-
Adj. Risk difference prec	-	-	Y	-	-
Adj. Risk difference MH	-	-	-	-	-
Odds-based point est/CIs
Crude OR
OR cross-product	Y	Y	Y	-	-
OR MLE	Y	Y	Y	-	-
Adjusted OR
Adj OR MH	Y	Y	Y	Y	Y
Adj OR precision	-	-	Y	Y	-
Adj OR MLE	Y	Y	Y	-	-
CI for adjusted OR
Taylor	-		Y	-	-
RGB	Y	Y	Y	Y	Y
Fisher	Y	Y	Y	Y	-
Mid-P	Y	-	Y	-	-

Note that Epi Info, SAS, and SPSS can estimate the OR MLE using logistic regression, and SAS can estimate an adjusted risk ratio and risk difference using PROC GENMOD

Comparison of Epi Info, OpenEpi, SAS, and SPSS for stratified 2x2 tables, person-time data

	Epi Info 3.5.4	Epi Info 7.1.4	OpenEpi 2.3.1	SAS 9.3	SPSS 17.0
Statistical Tests
Statistics for crude table	-	-	Y	-	-
Statistics for adjusted results
Z approach	-	-	1 & 2 sided	-	-
Fisher exact	-	-	1 & 2 sided	-	-
Mid-p exact	-	-	1 & 2 sided	-	-
Test for interaction (Woolf)
Rate ratio	-	-	Y	-	-
Rate difference	-	-	Y	-	-
Rate-based point est/CIs
Rate ratios
Crude Rate ratio	-	-	Y	-	-
Adj. Rate ratio MH	-	-	Y	-	-
Adj. Rate ratio precision	-	-	Y	-	-
Rate differences
Crude Rate difference	-	-	Y	-	-
Adj. Risk difference prec	-	-	Y	-	-
Adj. Risk difference MH	-	-	-	-	-

Another approach to analyzing person-time data is through survival analysis which Epi Info, SAS, and SPSS can perform